Like if it means that the observer in S' will measure a greater time interval, well howcome the observer in S doesn't, since one could equally say that he is moving relative to S'?

The formula is valid only if the two events happen at the same place in S, not in S'. It says that in this case, S' measures a longer time between the events than S, since y>1. Generally, the observer for which the two events happen at the same place measures the shortest time.